(How Paradigms Affect Science)


For over half a century cosmologists have been guided by the assumption that matter is distributed homogeneously on sufficiently large scales. On the other hand, observations have consistently yielded evidence for inhomogeneity right up to the limits of most surveys. This apparent paradox can be understood in terms of the role that paradigms play in the evolution of science.



Robert L. Oldershaw

Amherst College

Amherst, MA 01002







Modern cosmology dates from the early decades of this century when Einstein's field equations were first applied to the universe. Severe difficulties in solving these equations (10 nonlinear partial differential equations in 4 variables) led theorists to introduce various simplifying assumptions such as the postulate of cosmological homogeneity. This idea of a uniform cosmos did not represent a break from the past since the previous Newtonian paradigm hypothesized an infinite homogeneous universe. Unexpectedly, however, solutions of Einstein's equations seemed to suggest expanding or contracting universes, and even Einstein himself at first thought that these solutions were unrealistic. But before long astronomers confirmed that the observable portion of the universe did appear to be expanding uniformly.

At this point the assumption of cosmological homogeneity was still speculative since it could not be tested adequately. However, the rough concordance of the expanding universe model and preliminary observations of the cosmos gave astronomers confidence in their new concept of homogeneous expansion. Virtually all astronomers believed that future observations would reveal a highly uniform large-scale distribution of matter. Other problems, such as the initial state of the universe and how the early universe evolved, were more pressing concerns. Gradually the Big Bang model of the universe took shape and began to dominate the field of cosmology. This paradigm asserts that some 12 to 20 billion years ago all space, time and matter were packed inside a single mysterious entity called a singularity. A cosmological singularity is a mathematical point with no size at all, but having infinite density and temperature. If you have trouble imagining such an initial state, do not worry, it is beyond visualization. For unknown reasons, perhaps to stretch its legs a bit, the universe began to expand from its completely collapsed state. The expansion is not envisioned as an explosive event, but rather more like someone inflating a three dimensional balloon.

Once the temperature of the adibatically cooling matter became low enough, structures such as atoms, stars and galaxies could begin to gravitationally "condense" out of the high energy plasma. In the Big Bang model it is natural to expect that the uniform expansion would result in homogeneous distributions of background radiation and large-scale structures, so the simplifying assumption of homogeneity seemed quite secure. The envisioned cosmological homogeneity is not a virtually perfect homogeneity such as is found in a pure quartz crystal, but rather is a statistical homogeneity, which becomes more perfect as you increase the size of the observed volume. In astrophysics, one basic way to test for the presence of a homogeneous large-scale distribution of matter is to to check one vast volume for an even distribution of matter, radiation or motion. Another method is to select two smaller volumes of space and compare various characteristics of each sample, such as the number of a given class of objects.

In this essay we will see how the assumption of cosmological homogeneity underwent an unjustified transformation from a postulate to an "empirical fact", and how theoreticians have responded to the challenge of many observations that contradict the basic idea of large-scale homogeneity. This story is an interesting, and surprising, case study for Thomas S. Kuhn's well-known ideas about paradigmatic change and the evolution of science.




The concept of cosmological homogeneity started out as a reasonable guess about the universe, and as a mathematical device for making Einstein's equations more tractable. A few decades later, the physics/astronomy community treats cosmological homogeneity as an empirical fact. Since cosmology is recognized as a full-fledged science, one would expect that this metamorphosis from assumption to apparent fact would be strongly supported by several types of empirical evidence. The curious thing, however, is that such evidence does not exist. Over the years there were preliminary observations of galaxy distributions that were interpreted as supporting the homogeneity assumption. However, more refined experiments have shown that such conclusions were usually premature and incorrect. It is true that the microwave background radiation, which is interpreted as as a primordial remnant of matter formation, is cited as supporting the homogeneity assumption. However, there are other explanations for the origin of this radiation, and the microwave background has a decisive dipole anisotropy that may conflict with its use as evidence for homogeneity (if galactic streaming results indicate that the dipole is intrinsic and not a Doppler effect). Most importantly the microwave background argument for homogeneity is contradicted by the more direct evidence for structural inhomogeneity right up to observational limits. The microwave background may one day be powerful evidence for or against cosmological homogeneity, but for now it is safer to focus on the distribution of actual galactic-scale structures. As our ability to test the homogeneity assumption has improved, a consistent string of discoveries has favored cosmological inhomogeneity right up to the size limits of the surveys. Let us look at some of the evidence that has been grudgingly acknowledged in word, but effectively ignored in practice by many cosmologists.

The first serious challenge to the assumption of cosmological homogeneity came in the latter half of the 1920s when astronomers confirmed that stars were not homogeneously distributed, but rather were amassed in huge "island universes" which we now call galaxies. It was subsequently assumed that beyond the scale of individual galaxies, perhaps at 1 to 5 Mpc (where 1 Mpc = 3.26x106 light years), the large-scale distribution of galaxies became homogeneous. However it was not long before astronomers discovered that galaxies were inhomogeneously clustered into small groups of a few to several tens of galaxies. Theoreticians then hypothesized that the small galaxy clusters would be distributed homogeneously at scales of 20 to 30 Mpc. Before going further, it should be mentioned that all cosmological size measurements are uncertain by up to a factor of two due to uncertainties in the Hubble constant, which is intimately involved in determining cosmological distance scales.

As telescopes and data analysis improved, some observers believed that they were seeing inhomogeneous clustering well beyond the previous 30 Mpc limit, perhaps up to 50 Mpc. As a result, the debate over homogeneity versus inhomogeneity began to heat up during the 1970s. In a remarkable article that heralded much of what was to come ("The Case for a Hierarchical Cosmology", Science vol. 167, 1203-1213, 1970), Gerard de Vaucouleurs of the University of Texas at Austin presented evidence that small galaxy clusters were further clustered into "superclusters" on scales of 60 Mpc or greater. In virtually a lone voice of dissent he argued compellingly that there had never been valid evidence for the "empirical fact" of cosmological homogeneity. Most theoreticians, and the majority of all astronomers of the time, believed that inhomogeneity declined sharply at 20 Mpc and that homogeneity took over just beyond that size scale. The lopsided debate over the reality of superclustering and inhomogeneity at roughly 60 Mpc continued throughout the 1970s, with de Vaucouleurs and a minority of supporters eventually emerging as the victors.

Not surprisingly, proponents of cosmological homogeneity then predicted that large-scale uniformity would finally be found on scales of 60 to 100 Mpc. Once again, however, nature was to disappoint them. During the 1980s the observational evidence for nonuniformity at ever larger scales began to clamor for recognition and explanation. Technical advances led to larger and more detailed surveys of galaxy distributions and motions, and it became clear that inhomogeneity did not "decline sharply beyond 20 Mpc", but rather continued right up to the new observational limits. Surprisingly, galaxies appeared to be gathered into immense sheets and filaments surrounding very large bubble-like "voids", wherein the galaxy density was low. The large-scale structure had a mysterious frothy or cellular configuration.

By means of a new type of survey that measured the velocity vectors of galaxies (after general expansion had been subtracted out), it was found that galaxies within 65 Mpc, and later within 100 to 200 Mpc, were flowing in a coordinated manner in a particular direction. These bulk flows suggested that vast lumps of matter on even larger scales were responsible for directing these galactic flows. The most famous lump was dubbed "The Great Attractor". Observers chalked up a steady string of "largest" galaxy superclusters (200 Mpc, 300 Mpc, 360 Mpc, 400 Mpc, ...) and voids (100 Mpc, 200 Mpc, 300 Mpc, ...).

There were further observational discoveries that shocked nearly everybody. In one study published in Nature by P. Birch of the University of Manchester's Nuffield Radio Astronomy Laboratory at Jodrell Bank, classical double radio galaxies were found to have nonrandom position angles and polarization vectors on scales of 1,000 Mpc, far beyond the scale at which random behavior was supposed to have taken over. Another study, also published in Nature, by T. J. Broadhurst et al of the University of Durham, revealed evidence for periodic clustering of galaxies over a length scale of 2,000 Mpc. Both of these reports initially caused a flurry of excitement, with astronomers quoted as saying that the results were completely unexpected and required a sincere review of previous assumptions. However, even though subsequent experiments supported the initial findings, most theoretical astronomers and cosmologists reverted to their standard homogeneous models as soon as it seemed respectable to do so.

Toward the end of the 1980s the homogeneity/inhomogeneity debate had become a more even-handed affair, and the sides were more polarized than ever. Princeton's P.J.E. Peebles, usually one of the more moderate spokesmen for theoretical cosmologists stated in Physica D (vol. 38, 273, 1989), "I think the evidence for [large scale homogeneity] is close to compelling, though, it is fair to say, not definitive." Observational astronomers were more inclined to agree with the conclusions of B.R. Tully, of the University of Hawaii (Science vol. 238, 894, 1987): "A decade ago, we'd have thought that as we went to larger scales we'd see more homogeneity in the universe. In fact, we see more inhomogeneity." Those who saw evidence for inhomogeneity right up to the largest scales surveyed tended to think that we really did not understand the large-scale universe very well at all. Theoreticians, on the other hand, had considerable faith in their models and believed that they nearly had the universe figured out. Such radically differing interpretations of the same data naturally led to tension in the astrophysical community.

During the 1990s, the patterns set in the 1980s have continued: inhomogeneity has been discovered on ever-larger scales and the hypothesis of homogeneity has continued its strategic retreat. The reality of structures and voids in the 100 Mpc to 400 Mpc range has now been established. The periodic clustering over scales on the order of 103 Mpc, discovered by Broadhurst et al, has been backed up by subsequent experiments. The "Great Attractor" has been dethroned by the even larger "Great Wall", a vast and roughly linear agglomeration of galaxy clusters in the northern hemisphere. A surprisingly similar counterpart, the "Southern Wall", has recently been discovered in the southern hemisphere. The evidence for large-scale inhomogeneity has been reviewed perceptively by P. H. Coleman of the University of Leiden and L. Pietronero of the University of Rome (Physics Reports vol. 213, 311, 1992). They argue that the proposed evidence in favor of cosmological homogeneity is "based on methods of analysis that assume it implicitly". A more objective study of the data has convinced them that evidence for nonuniformity persists right up to the limits of all surveys, such that there is no credible evidence for convergence to homogeneous distributions.

The response of those who have long favored homogeneous models of the universe has been quite interesting. They confidently assert in books and scientific papers that the universe simply must be homogeneous, if not at 60 Mpc then surely at 100 Mpc or somewhere beyond that. One must infer that these scientists do not take a great deal of interest in the observational evidence for cosmological inhomogeneity that has been accruing over the last two decades. We have here a somewhat unusual state of affairs with two groups of scientists describing the same universe in two very different ways. One group is seriously thinking that a "theory of everything" could be just around the corner, while the other group is worried that some of our key cosmological assumptions that have been embraced for decades are probably wrong, and that our understanding of the cosmos is far less comprehensive.




How is it possible that these two groups can arrive at such mutually exclusive conclusions? Actually, this paradoxical state of affairs regarding cosmological homogeneity is not that hard to understand. When humans repeatedly use an assumption or model it gradually becomes transformed into "fact". In perhaps the best known treatise on scientific evolution, entitled The Structure of Scientific Revolutions, Thomas S. Kuhn documents how scientists become so steeped in a paradigm that healthy skepticism about assumptions and models tends to disappear. What begins as speculation metamorphoses into common sense and self-evident truth. Usually this is supported by tentative evidence that, with all good intentions, is subtlely shaped to fit theoretical desires. On the other hand, contradictory evidence is all too often ignored or belittled. For example, one cosmologist referred to recent evidence solidly lining up behind inhomogeneity as "anecdotal." Scientists tend to look for and find what they expect to find; it is far more difficult to recognize the importance of results that are not expected.

Such an impasse is the norm when a new scientific paradigm challenges an old one. Paradigmatic consensus is usually very beneficial to science in that it organizes knowledge and coordinates scientific activity. But unfortunately there is a problematic side to the consensus approach. Scientists who have studied, conducted research, and made their scientific mark under the guidance of a paradigm are often confined to its conceptual limits. Competing paradigms sound decidedly wrong; the new hypotheses seem to be to self-evident violations of scientific knowledge. Moreover, competing paradigms represent a threat to one's professional status and one's sense of intellectual security. A changeover of paradigms requires people to give up deeply held beliefs and to accept new ones that sound somewhat outrageous. Obviously this is not something that comes easily to us.

The debate over the legend of cosmological homogeneity may be symptomatic of an on-going , slow-motion, revolution in cosmology. Major contests between old and new paradigms are not fought and won quickly, but rather are more like the collisions of two glaciers. The more massive one will eventually overpower the other, but the action is slow-paced and at times it is not clear which side has the momentum. Will the theoreticians' dream of a homogeneous cosmos finally emerge before the survey limits reach to the edges of the observable universe, or will the 50 year old trend of inhomogeneity on ever-larger scales continue unabated? Do we know nearly everything about the universe or are we still groping for a basic understanding? Time will tell.

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